Question

Find the area of the segment $AYB$. shown in the adjacent fig. Given radius of the circle is $21cm$ and $<AOB={120}^{\circ }$c(Use $\pi =\frac{22}{7},\sqrt{3}=1.732$)

Answer 1

The area of segment is given as area of sector -area of triangle

Radius of circle is $21cm$

The angle at center is ${120}^{\circ }$

Area of sector is $\frac{x}{360}\times \pi \times r\times r$
$=\frac{120}{360}\times \frac{22}{7}\times 21\times 21$
$=22\times 21=462c{m}^2$

Area of triangle $\frac{1}{2}ab\sin \theta$
$=\frac{1}{2}\times 21\times 21\sin 120$
$=\frac{441\sqrt{3}}{4}=190.953$

Area of segment is $=462-190.953=271.047c{m}^2$